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Working with a two-factor APT model an investor has found two risk factors, X and Y. The investor...

Working with a two-factor APT model an investor has found two risk factors, X and Y. The investor is looking at two stocks, A and B. The expected return on stock A is 12% and that of stock B 10%. The beta (factor sensitivity) of stock A with respect to X is 1 and with respect to Y it is 1/2. The beta of stock B with respect to X is 0 and with respect to Y it is 2. The risk free rate is 4%. What are the risk premia of factors X and Y?

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expected return = risk free rate +beta 1*factor 1 + beta 2 *factor 2

for stock A

12=4+1*X+1/2*Y

for stock B

10 = 4+0*X+2*Y

Y = 3

substituting value of Y in stock X equation

12=4+1*X+1/2*3

X = 6.5

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